This is the same as the similarly named achievement from the original 360 version.
Here is the original solution from M Monster D.
This Achievement is story related and can't be missed.
Unlike other story achievements in the game this mission (attack of Clones) is required to play to stop you from having a standard notoriety and get attacked by random AI's. Once this mission unlocks I recommend you to immediately knock this of the list to prevent the AI from messing with your business.
*** Spoiler - click to reveal ***The achievement unlocks after you the defeated the Saints Row 1 clone followed up by the Saints Row 2 co-op clones. You just need to throw them in the portal once you've damaged them enough.